Learning Forum

[haoyang]

Hi,

I am simulating the diffractions of a 2D sinusoidal grating (period along x and y direction is 8 microns) at different incident angles (normal incidence, 15 degrees, 30 degrees, ...) and different wavelengths (e.g., 450 nm, 520 nm, and 630 nm, all visible lights). I followed this official example: Diffraction grating.

In this official example, it simulates the diffraction of 2D grating with broadband (0.85 to 1 um) plane wave at normal incidence. I have the following 3 questions:

1. At the normal incidence situation, the total transmitted power + total reflected power is very close to 1 (T + R = 0.995), which obeys the energy conversion (assuming no material loss). However, when I set the incident light is obliquely incident (theta = 15 degrees), I found the T + R = 0.9. I am wondering where the 10% incident light energy comes to. I have set the light source with BFAST condition.
2. I am going to simulate the incident angle at 0 degrees to 80 degrees, step is 10 degrees. However, when the incident angle is larger than 40 degrees. The estimated simulation time increases a lot and the FDTD Lumerical reminds steep angle for BFAST is very tricky. (I found a related post to this)
3. Since I doesn't need broadband light source, just simulating selected wavelengths, in this case, could I use single wavelength light source and use bloch BC for oblique incidence to save simulation time?

I really appreciate your time and help!

Best regards,

Hao

[Guilin Sun]

A1: please check if the structure material has loss. Normal incidence and oblique have different losses. It may also mean the simulation time not long enough or autoshutoff min is not small enough. Please refer Ansys Insight: 为什么说仿真时间要足够长才能得到正确的频域结果 A2: PML performance can be degraded as the incident angle or scattering angle is large. So you may need to use different type of PMLs, or use different number of layers. It can be difficult to use one PML for normal incidence to 80 deg. In particular, 80 deg is quite large for most PML settings. You are right that at very large incident angle the simulation time can be very long, due to its inherent limitation of this method. When I wrote that article, I did some tests. A3: if you only have a few of wavelengths, using Bloch+ single wavelength might be a better choice. You can sweep those wavelengths. Please try.

[haoyang]

Hi, Thank you so much for your quick reply! The figure below shows the structure of my 2D sinusoidal grating. The periods along the x and y directions are 8 microns. The index of my material at 550 nm is 1.62, while the background index is 1.47. There is a 10 microns thick layer below the 2D grating structure. Since I want to see the reflection and transmission in the background index, my current FDTD region is 8 um * 8 um * 14 um. The BC along x and y directions are bloch, the BC at z and -z directions are PML. I have 2 questions:

1. Because the entire thick layer is included in the FDTD region, the simulation time will be very long. Do you have an equivalent method to replace this 10 microns thick layer in order to save simulation time?
2. Since I need to do the simulation at oblique incidence, will the above equivalent way still be effective at oblique incidence?

I really appreciate your time and help!

[Guilin Sun]

A1: No need to include the 10um long, as its back end may only have Fresnel loss, which you can correct the transmission later. You can also develop an algorithm to take this cavity into consideration. This is more a theoretical work. But you can try one or two simulations to include it and compare the cases with truncated substrate by PML. This 10um substrate may be supported by another material, such as glass. otherwise it is so thin and can be fragile. A2: Oblique incidence works fine w/o the substrate end surface. The problem is, if you want to count the back end effect, since now the grating-back-end forms a cavity, simulation should be long enough to let the pulse decays sufficiently with enough round-trips. Thus it needs long simulation time.

[haoyang]

Hi, Thank you so much for your quick reply! The actual thickness of the layer will be 30 microns while not 10 microns. I just set it as 10 microns to run the initial simulation. To make the Autoshutoff around 10^-6, the simulation time is around 2 hours. Is there an example I can follow to develop an algorithm by considering this cavity? Thanks a lot!

[Guilin Sun]

You can have a comparison:

1: when I say broadband, you may need to use BFAST, incident angles under 60 deg would be better.

2: if you only need a few wavelengths, both Bloch FDTD and RCWA works fine.

Please try.

[haoyang]

You can have a comparison:

1: when I say broadband, you may need to use BFAST, incident angles under 60 deg would be better.

2: if you only need a few wavelengths, both Bloch FDTD and RCWA works fine.

Please try.

[Guilin Sun]

You can have a comparison:

1: when I say broadband, you may need to use BFAST, incident angles under 60 deg would be better.

2: if you only need a few wavelengths, both Bloch FDTD and RCWA works fine.

Please try.

[haoyang]

You can have a comparison:

1: when I say broadband, you may need to use BFAST, incident angles under 60 deg would be better.

2: if you only need a few wavelengths, both Bloch FDTD and RCWA works fine.

Please try.

[Guilin Sun]

You can have a comparison:

1: when I say broadband, you may need to use BFAST, incident angles under 60 deg would be better.

2: if you only need a few wavelengths, both Bloch FDTD and RCWA works fine.

Please try.